SOLUTION: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decode
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Question 1163782: Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?
Found 3 solutions by ikleyn, solver91311, greenestamps:
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
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P = = = . ANSWER
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability that the first box that is chosen has the right gift is the number of boxes that have the gift you want divided by the total number of boxes on the shelf. Given that the first box actually has the right thing, then when you choose the second box, there is one less box that has the right gift and one less box total, changing the probability on the second draw. Since you have accounted for the change in values from one draw to the other, the events are independent and the multiplication rule applies.
John
My calculator said it, I believe it, that settles it
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
P(first box has a decoder ring) = 18/52
P(second box has a decoder ring) = 17/51
P(both have decoder rings) = (18/52)*(17/51) = (9/26)(1/3) = 3/26
OR....
Using a more sophisticated method -- which might be required in similar but more complicated problems....
P(both have decoder rings) = (# of ways of choosing 2 of the 18 boxes with decoder rings) divided by (# of ways of choosing 2 of the 52 boxes)
=
which is the same calculation as by the more elementary method.
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